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Computing Walrasian Equilibria: Fast Algorithms and Structural Properties [article]

Renato Paes Leme, Sam Chiu-wai Wong
2016 arXiv   pre-print
We present the first polynomial time algorithm for computing Walrasian equilibrium in an economy with indivisible goods and general buyer valuations having only access to an aggregate demand oracle, i.e  ...  We also give the fastest known algorithm for computing Walrasian equilibrium for gross substitute valuations in the value oracle model.  ...  Murota and Tamura [MT03] give combinatorial algorithms for the problem of computing Walrasian equilibria via a reduction to the M -convex submodular flow problem.  ... 
arXiv:1511.04032v2 fatcat:tharcfrx65b4xnr7y4nonpxuei

Computing Walrasian equilibria: fast algorithms and structural properties

Renato Paes Leme, Sam Chiu-wai Wong
2018 Mathematical programming  
We present the first polynomial time algorithm for computing Walrasian equilibrium in an economy with indivisible goods and general buyer valuations having only access to an aggregate demand oracle, i.e  ...  We also give the fastest known algorithm for computing Walrasian equilibrium for gross substitute valuations in the value oracle model.  ...  Comparison to related work Iterative auctions and subgradient algorithms The first algorithm for computing Walrasian equilibria in an economy of indivisible goods is due to Kelso and Crawford [21] and  ... 
doi:10.1007/s10107-018-1334-9 fatcat:fytimwept5dejbxc4i5qvvpk4e

Solving Deterministic and Stochastic Equilibrium Problems via Augmented Walrasian

Julio Deride, Alejandro Jofré, Roger J-B Wets
2017 Computational Economics  
We described a method to solve deterministic and stochastic Walras equilibrium models based on associating with the given problem a bifunction whose maxinf-points turn out to be equilibrium points.  ...  In the dynamic versions of our models, deterministic and stochastic, we are mostly concerned with models that equip the agents with a mechanism to transfer goods from one time period to the next, possibly  ...  We thank David Woodruff, University of California Davis, for his assistance with Pyomo, the optimization modeling language used in the computational implementation of our algorithm.  ... 
doi:10.1007/s10614-017-9733-1 fatcat:g5okmtfpc5eunnxsa2wjwkcdua

Approximation of Walrasian equilibrium in single-minded auctions

Li-Sha Huang, Minming Li, Bo Zhang
2005 Theoretical Computer Science  
We show NP-hardness of the optimization problem, establish lower and upper bounds of R, as well as develop greedy algorithms to approximate the optimal value of R.  ...  We consider a social optimization model of pricing scheme in single-minded auctions, in cases where Walrasian equilibrium does not exist.  ...  [3] developed a fast algorithm to achieve the equilibrium for the cases with nice structures and proved the NP-hardness for the general case.  ... 
doi:10.1016/j.tcs.2005.03.008 fatcat:66rb3hdqfjdtdbphsqnu4m6fbi

On Approximate Welfare- and Revenue-Maximizing Equilibria for Size-Interchangeable Bidders [article]

Enrique Areyan Viqueira, Amy Greenwald, Victor Naroditskiy
2017 arXiv   pre-print
In a Walrasian equilibrium (WE), all bidders are envy-free (EF), meaning that their allocation maximizes their utility; and the market clears (MC), meaning that the price of unallocated goods is zero.  ...  Instead of computing an outcome that simultaneously yields an allocation and corresponding prices, one could first solve for an allocation that respects a reserve price, and then solve for a corresponding  ...  paves the way for fast computational methods to nd such outcomes.  ... 
arXiv:1708.03097v1 fatcat:ml5l7ake4raz3hyrwtni4a6nt4

A global Newton method to compute Nash equilibria

Srihari Govindan, Robert Wilson
2003 Journal of Economic Theory  
A new algorithm is presented for computing Nash equilibria of¯nite games.  ...  The algorithm is outlined and computational experience is reported. JEL Classi¯cation C63.  ...  games (RosenmÄ uller, 1971 ; Wilson, 1971) , and applications to Walrasian equilibria of economic models (Balasko, 1988; Eaves and Schmedders, 1999 , and their extensive references; Scarf and Hansen  ... 
doi:10.1016/s0022-0531(03)00005-x fatcat:fimnz7mftrbltc6tkwuqvgqvgi

Chapter 38 Computation and multiplicity of equilibria [chapter]

Timothy J. Kehoe
1991 Handbook of Mathematical Economics  
Thus, if we had an algorithm for computing equilibria of arbitrary economies specified in terms of preferences and endowments, using it to compute fixed points would be complicated.  ...  A simple extension of our previous argument demonstrates the existence of equilibrium in a production technology and suggests algorithms for computing equilibria.  ... 
doi:10.1016/s1573-4382(05)80013-x fatcat:as5rsx26m5eedpwczmg36ninmu

The Price is (Probably) Right: Learning Market Equilibria from Samples [article]

Omer Lev, Neel Patel, Vignesh Viswanathan, Yair Zick
2021 arXiv   pre-print
We consider the setting where player valuations are unknown; using a PAC learning-theoretic framework, we analyze some classes of common valuation functions, and provide algorithms which output direct  ...  Equilibrium computation in markets usually considers settings where player valuation functions are known.  ...  Brânzei et al. (2016) present an Algorithm to compute equilibria under equal budgets. We extend this Algorithm to settings where each player has a unique budget. Theorem 5.2.  ... 
arXiv:2012.14838v2 fatcat:fw6thtnmurad5jfn5a73d2xree

A Hydraulic Approach to Equilibria of Resource Selection Games [article]

Yannai A. Gonczarowski, Moshe Tennenholtz
2016 arXiv   pre-print
., asymmetric singleton congestion games) with nonatomic players, the coincidence of strong equilibria and Nash equilibria in such games, and the uniqueness of the cost of each given resource across all  ...  -dependent weighting, is defined, and the results are extended to this family, showing the existence of strong equilibria, and showing that while resource costs are no longer unique across Nash equilibria  ...  the structure of the input, this may render the complexity of this computation exponential in the encoded input size.  ... 
arXiv:1403.7605v7 fatcat:eaitof23braozhlavgdc34erve

A Consumer-Theoretic Characterization of Fisher Market Equilibria [article]

Denizalp Goktas, Enrique Areyan Viqueira, Amy Greenwald
2022 arXiv   pre-print
The main tools we use are the dual concepts of expenditure minimization and indirect utility maximization.  ...  We then prove that the subdifferential of the dual of our convex program is equal to the negative excess demand in the associated market, which makes generalized gradient descent equivalent to computing  ...  A detailed inquiry into the computational properties of market equilibria was initiated by Devanur et al.  ... 
arXiv:2107.08153v2 fatcat:ic3xhujysvdtlfmbnwi4ltgxsq

A Hydraulic Approach to Equilibria of Resource Selection Games

Yannai A. Gonczarowski, Moshe Tennenholtz
2016 Proceedings of the 2016 ACM Conference on Economics and Computation - EC '16  
., asymmetric singleton congestion games) with nonatomic players, the coincidence of strong equilibria and Nash equilibria in such games, and the uniqueness of the cost of each given resource across all  ...  , and showing that while resource costs are no longer unique across Nash equilibria in games of this family, they are nonetheless unique across all strong Nash equilibria, drawing a novel fundamental connection  ...  the structure of the input, this may render the complexity of this computation exponential in the encoded input size.  ... 
doi:10.1145/2940716.2940749 dblp:conf/sigecom/GonczarowskiT16 fatcat:qczyferbgnbhjf2xi5hiqn3nvu

The Complexity of Exchange*

Robert Axtell
2005 Economic Journal  
Recent results on the computational complexity are reviewed. The non-polynomial complexity of these algorithms makes Walrasian general equilibrium an implausible conception.  ...  The computational complexity of two classes of market mechanisms is compared. First the Walrasian interpretation in which prices are centrally computed by an auctioneer.  ...  In particular, k-lateral exchange equilibria have much better computational complexity than do Walrasian equilibria.  ... 
doi:10.1111/j.1468-0297.2005.01001.x fatcat:gxdo72yw2ffp5oabztktfjeglu

Page 1608 of Mathematical Reviews Vol. , Issue 87c [page]

1987 Mathematical Reviews  
Preckel, Paul V. (1-PURD) 87c:90048 Alternative algorithms for computing economic equilibria. Economic equilibrium: model formulation and solution. Math. Programming Stud. No. 23 (1985), 163-172.  ...  We demonstrate that if the probability that agents are linked with each other does not tend to zero too fast as this number increases, then the probability that a coalition will form and block any non-Walrasian  ... 

Complexity Theory, Game Theory, and Economics: The Barbados Lectures [article]

Tim Roughgarden
2019 arXiv   pre-print
It consists of two five-lecture sequences: the Solar Lectures, focusing on the communication and computational complexity of computing equilibria; and the Lunar Lectures, focusing on applications of complexity  ...  19--23, 2017, as the 29th McGill Invitational Workshop on Computational Complexity.  ...  problem that is hard and yet structured enough to be solved using approximate Nash equilibrium computation.  ... 
arXiv:1801.00734v2 fatcat:r6sz7jskqjbs7gxof52fbjikom

Decoupling Markets and Individuals: Rational Expectations Equilibrium Outcomes from Information Dissemination Among Boundedly-Rational Traders

Karim Jamal, Michael Maier, Shyam Sunder
2012 Social Science Research Network  
structural properties of markets.  ...  These findings suggest that market structure is an important determinant of efficient aggregate level outcomes, and that care is necessary not to overstate the importance of human cognition and conscious  ...  This control allows us to hold trader "cognition" constant at a specified level and explore the outcome properties of market structures and environment.  ... 
doi:10.2139/ssrn.2120019 fatcat:kkr2qlqufvewvggbgayetaoo6q
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